MinT - Best Known (125−33, 125, s)-Nets in Base 5

Best Known (125−33, 125, s)-Nets in Base 5

(125−33, 125, 400)-Net over F₅ — Constructive and digital

Digital (92, 125, 400)-net over F₅, using

9 times m-reduction [i] based on digital (92, 134, 400)-net over F₅, using
- trace code for nets [i] based on digital (25, 67, 200)-net over F₂₅, using
  - net from sequence [i] based on digital (25, 199)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
      - a function field by GarcÃa and Quoos [i]

(125−33, 125, 1734)-Net over F₅ — Digital

Digital (92, 125, 1734)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(125−33, 125, 444104)-Net in Base 5 — Upper bound on s

There is no (92, 125, 444105)-net in base 5, because

1 times m-reduction [i] would yield (92, 124, 444105)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 470 208854 172764 706993 737410 818602 838522 298690 567784 098664 448614 259838 081853 508899 099585 > 5¹²⁴ [i]